In the airliners,
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The first to ever come on are the position (nav) lights. These are the green/white and red/white lights (whites at the back). They signify that the airplane is electrically energized. Depending on time of day, the logo lights can come on at this time too.
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Then comes the beacon. You turn these on to let the ground crew know that the aircraft is about to move or be moved (towed). You turn them on before starting the APU. This light remains on the entire flight, you turn it off after the aircraft has come to rest and APU is off.
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Taxi lights and runway turn-off lights: you turn these on before beginning your taxi. More on this later.
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Strobes: turn these on before ever entering or crossing the runway. Remains on the entire flight. Turn off after exiting the runway after landing.
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Landing lights: you turn these on before entering the runway, turn off above 10,000 feet. Back on as soon as you get to 10,000 and leave on until you exit the runway after landing.
For the taxi lights, combine with landing lights for takeoffs and landings. What some airlines do is, when you’re cleared to line up and wait, then turn on landing lights and turn off taxi as a reminder that although you’ve been cleared onto the runway, you’ve not been cleared for takeoff. Turn on as soon as you receive clearance for takeoff.
On approach, wait until final clearance to land, then taxi lights on. Leave on until you’re about to turn into your gate or ramp, then turn off to avoid blinding the ground crew. Always combine the taxi and runway turn-off. When going unto the runway, all lights on.